def test_pred_interval(show_plot=False):
from ml_ext import examples
(coefs,df)=examples.gen_simplemodel_data(n=50,k=3)
df.sort('X1',inplace=True)
lr=LinModel()
X=df[df.columns[df.columns!='y']]
y=df.y
lr.fit(X=X,y=y)
lr.summary()
df_ci=lr.get_confidence_interval_for_mean(X)
df_pi=lr.get_prediction_interval(X)
#Now use statsmodels to compare
from statsmodels.sandbox.regression.predstd import wls_prediction_std
import statsmodels.api as sm
re = sm.OLS(y, X).fit()
prstd, iv_l, iv_u = wls_prediction_std(re)
if show_plot:
(fig,ax)=plt.subplots(nrows=2,ncols=1,figsize=[14,12])
cols=sns.color_palette('husl',n_colors=4)
ax[0].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[0].plot(X.X1,df_pi['upper_pred'],label='pred',color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_pi['lower_pred'],color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_ci['upper_mean'],color=cols[2],alpha=0.5)
ax[0].plot(X.X1,df_ci['lower_mean'],label='mean_ci',color=cols[2],alpha=0.5)
ax[0].scatter(X.X1,df_pi['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[0].legend(loc='best')
ax[1].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[1].scatter(X.X1,df_ci['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[1].plot(X.X1,iv_u,label='wls',color=cols[1],alpha=0.5)
ax[1].plot(X.X1,iv_l,color=cols[1],alpha=0.5)
ax[1].legend(loc='best')
#get difference between uppers from each and check they are within 1%
overall_diff=100*numpy.sum(iv_u-df_pi['upper_pred'])/numpy.sum(iv_u)
logging.debug("Overall % difference in prediction ranges for upper bound: {}".format(overall_diff))
assert overall_diff<0.1
def fit(self, X, y, n_jobs=1):
"""
y can be series or array
X can be dataframe or ndarry (N datapoints x M features)
"""
self = super(LinModel, self).fit(X, y, n_jobs)
self.nobs=X.shape[0]
self.nparams=X.shape[1]
#remove an extra 1 for the alpha (k-1)
self.df_model=X.shape[1]-1
#(n-k-1) - we always assume an alpha is present
self.df_resid=self.nobs-X.shape[1]-1
#standard error of the regression
y_bar=y.mean()
y_hat=self.predict(X)
self.raw_data=X
self.training=y
# logging.debug(X)
self.fittedvalues=y_hat
#explained sum of squares
SSE=numpy.sum([numpy.power(val-y_bar,2) for val in y_hat])
e=numpy.matrix(y-y_hat).T
self.resid=numpy.ravel(e)
# logging.debug(y_bar)
# logging.debug(y)
SST=numpy.sum([numpy.power(val-y_bar,2) for val in y])
SSR=numpy.sum([numpy.power(x,2) for x in e])
self.ssr=SSR
#print(SSR)
#mean squared error of the residuals (unbiased)
#square root of this is the standard error of the regression
s_2 = SSR / (self.df_resid+1)
self.s_y=numpy.sqrt(s_2)
self.RMSE_pc=metrics.get_RMSE_pc(y,y_hat)
# logging.debug("s_y = {}".format(self.s_y))
#Also get the means of the independent variables
if isinstance(X,pd.core.frame.DataFrame):
#assume its' called alpha
self.X_bar=X[X.columns[X.columns!='alpha']].mean()
Z=numpy.matrix(X[X.columns[X.columns!='alpha']])
else:
#assume its the first column
self.X_bar=numpy.mean(X.values,axis=0)[1:]
Z=numpy.matrix(X[:,1:])
i_n=numpy.matrix(numpy.ones(self.nobs))
M_0=numpy.matrix(numpy.eye(self.nobs))-numpy.power(self.nobs,-1)*i_n*i_n.T
self.Z_M_Z=Z.T*M_0*Z
# #print(numpy.sqrt(numpy.diagonal(sse * numpy.linalg.inv(numpy.dot(X.T, X)))))
# #standard error of estimator bk
X_mat=numpy.matrix(X.values)
#print(X_mat)
self.X_dash_X=X_mat.T*X_mat
# we get nans using this approach so calculate each one separately
# se=numpy.zeros(self.nparams)
# for ii in range(self.nparams):
# se[ii]=numpy.sqrt(X_dash_X[ii,ii]*s_2)
# logging.debug(s_2)
# logging.debug(numpy.linalg.inv(X_dash_X))
# #se = numpy.sqrt(numpy.diagonal(s_2 * numpy.linalg.inv(numpy.matrix(X.T, X))))
se=numpy.sqrt(numpy.diagonal(s_2 * numpy.linalg.inv(self.X_dash_X)))
self.se= se
self.t = self.coef_ / se
self.p = 2 * (1 - stats.t.cdf(numpy.abs(self.t), y.shape[0] - X.shape[1]))
self.independent_ = []
if isinstance(X,pd.DataFrame):
self.independent_=X.columns.values
#t_val=stats.t.ppf(1-0.05/2,y.shape[0] - X.shape[1])
#R2 - 1-SSR/SST
self.rsquared=1-SSR/SST
#adjusted r2
#1-[(1-R2)(n-1)/(n-k-1)]
self.rsquared_adj=1-(((1-self.rsquared)*(self.nobs-1))/self.df_resid)
#f-value
f_value=(self.rsquared/(self.df_model))/\
((1-self.rsquared)/(self.df_resid+1))
self.f_stat=f_value
self.f_pvalue=stats.f.pdf(f_value,self.df_model,self.df_resid+1)
